Well, any computer ultimately executes a program (a computation, to be more accurate), whether it is hard-wired in the hardware (as in an ASIC) or not. If you create an ASIC to compute 1 + 1 and it outputs 2, but you later find out that you needed an ASIC that computed 1 - 1, I would not call that a hardware problem, because the hardware is doing exactly what it was supposed to do - it's just not useful to you. A hardware problem is one where your 1+1 ASIC is outputting 3 when it gets hot enough, or one where the ASIC is not starting at all.
Another piece of evidence that suggests to me that certain psychiatric conditions originate not in the physical brain itself but more in the "computation" (what I called a software error earlier) is the way people can be trapped into cults or other abusive relationships, where they start exhibiting signs of mental illness without any direct physical changes (that is, no diet changes, no physical violence, no irradiation etc.).
The reason why I consider this distinction is important is that, if I am right, then there must be psychiatric conditions that should be fixable through discussion and improvements in thinking (therapy), and there must also be psychiatric conditions that can't be fixed in this way. We know for sure that the second category exists, as some psychiatric symptoms are the result of tumors in the brain and elsewhere in the body; the first category is slightly less clear, thought therapy is definitely an important part of many treatment regimens, with clinical data backing up its use.
The biggest problem today is that we can't reliably tell, in most cases, which type of disease you may have, and so which approach is appropriate.